answer:The geometric mean of a set of numbers is the nth root of the product of the numbers, where n is the number of numbers in the set. In this case, we have six numbers, so the geometric mean is the sixth root of the product of the numbers. The product of the numbers is: 16 times 1 times (-1) times (-216) times (-59049) times 81 = -6,227,020,800 The sixth root of this number is: sqrt[6]{-6,227,020,800} = 18 sqrt[6]{2} 3^{5/6} Therefore, the geometric mean of 16, 1, -1, -216, -59049, and 81 is 18 sqrt[6]{2} 3^{5/6}. The answer is 18 sqrt[6]{2} 3^{5/6}

answer:The reduced row echelon form (RREF) of the matrix is: left( begin{array}{ccccc} 1 & 0 & 0 & 0 & -frac{5402}{4047} 0 & 1 & 0 & 0 & frac{4310}{4047} 0 & 0 & 1 & 0 & -frac{1697}{1349} 0 & 0 & 0 & 1 & frac{726}{1349} end{array} right)

answer:The (pseudo)inverse of the given matrix is: [ left( begin{array}{ccc} -frac{22}{43} & -frac{10}{43} & frac{20}{43} frac{9}{86} & frac{4}{43} & frac{11}{172} frac{1}{86} & frac{10}{43} & -frac{37}{172} end{array} right) ] I have verified the calculation, and the answer is correct.

answer:Given information: Annual end-of-year deposit = 500 Number of deposits (N) = 9 Annual interest rate (I) = 11% To calculate the future value of these deposits, we can use the following formula: Future value = Annual deposit × [(1 + I)^N - 1] / I Plugging in the given values, we get: Future value = 500 × [(1 + 0.11)^9 - 1] / 0.11 Future value = 500 × [2.416397 - 1] / 0.11 Future value = 500 × 14.16397 Future value = 7,081.99 Therefore, the future value of these deposits at the end of 9 years is 7,081.99.